Teksavvy doesn't have anything to do with your modem getting online, or IP assignments on your account. All they see is a bunch of traffic from thousands of customers on a POI. Teksavvy does give Rogers bundles of IP addresses for specific neighbourhoods to use. That's all Teksavvy does, everything else is Rogers.
At some point I'll type up the entire sync process, but for now I don't have time... What you need to do:
Disconnect your cable modem from the coax cable. This stops information about what's connected to the modem from getting to Rogers. It also starts a countdown for Rogers to clear all cached information about your connected devices.
Pick a router that you think is most likely to work. Connect it to the modem and power and factory reset it (get rid of any MAC cloning you may have done in the past). Modem is still not connected to coax.
Reboot everything, just to be sure. Modem is still not connected to coax.
Access 192.168.100.1, and you should get the modem config page. This is through the router, and the coax is still disconnected. (Problems? Access the status page of the router. Does it show a 192.168.100.x IP address for the WAN or Internet interface?)
Do the factory reset in the modem (sounds like you have a SB612X, and you need to do "Restore All Defaults" on the Configuration page). Modem is still not connected to coax.
Reboot everything again. Modem is still not connected to coax.
At this point you can attach the coax and wait for sync lights. Once the modem is fully synced you may have to reboot the router again.
If that doesn't work, do it all again except don't reconnect the coax for 30 minutes.--